scholarly journals Mixed Stochastic Differential Equations: Existence and Uniqueness Result

2016 ◽  
Vol 31 (2) ◽  
pp. 1119-1141 ◽  
Author(s):  
José Luís da Silva ◽  
Mohamed Erraoui ◽  
El Hassan Essaky
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals Periodic Solutions for Stochastic Differential Equations Driven by General Counting Processes: Application to Malaria

2021 ◽  
Vol 13 (4) ◽  
pp. 1
Author(s):  
KOUAME Yao Simplice ◽  
NZI Modeste
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Uniqueness Result ◽  
Poisson Processes ◽  
Counting Processes ◽  
Periodic Environment

In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with т-periodic stochastic intensity of time t has been given, for some  т> 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.

Well-posedness of Stratonovich multi-valued SDEs driven by semimartingales

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005
Author(s):  
Jing Wu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Change ◽  
Random Time ◽  
Approximation Technique ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Random Time Change

In this paper we consider Stratonovich type multi-valued stochastic differential equations (MSDEs) driven by general semimartingales. Based on an existence and uniqueness result for MSDEs with respect to continuous semimartingales, we apply the random time change and approximation technique to prove existence and uniqueness of solutions to Stratonovich type multi-valued SDEs driven by general semimartingales with summable jumps.

scholarly journals Solutions and comparison theorems for anticipated backward stochastic differential equations with non-Lipschitz generators

2016 ◽  
Vol 12 (4) ◽  
pp. 6139-6147
Author(s):  
Xuecheng XU ◽  
Min Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Comparison Theorems ◽  
One Dimensional

This paper is devoted to solving multidimensional anticipated backward stochastic differential equations (anticipated BSDEs for short) with a kind of non-Lipschitz generators. We establish the existence and uniqueness result for L2 solutions of this kind of anticipated BSDEs, and establish the corresponding one-dimensional comparison theorems for the type of anticipated BSDEs. Our results improve some known results.

scholarly journals Weak solutions to Vlasov–McKean equations under Lyapunov-type conditions

2019 ◽  
Vol 19 (06) ◽  
pp. 1950042 ◽  
Author(s):  
Sima Mehri ◽  
Wilhelm Stannat
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Total Variation ◽  
Existence And Uniqueness ◽  
Wasserstein Distance ◽  
Uniqueness Result ◽  
Total Variation Distance ◽  
Uniqueness Results ◽  
General Law ◽  
Variation Distance

We present a Lyapunov-type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature, most results concerning existence and uniqueness are obtained under regularity assumptions of the coefficients with respect to the Wasserstein distance. Some existence and uniqueness results for irregular coefficients have been obtained by considering the total variation distance. Here, we extend this approach to the control of the solution in some weighted total variation distance, that allows us now to derive a rather general weak uniqueness result, merely assuming measurability and certain integrability on the drift coefficient and some non-degeneracy on the dispersion coefficient. We also present an abstract weak existence result for the solution of law-dependent stochastic differential equations with merely measurable coefficients, based on an approximation with law-dependent stochastic differential equations with regular coefficients under Lyapunov-type assumptions.

scholarly journals Backward stochastic differential equations with stochastic monotone coefficients

2004 ◽  
Vol 2004 (4) ◽  
pp. 317-335 ◽  
Author(s):  
K. Bahlali ◽  
A. Elouaflin ◽  
M. N'zi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Nonlinear Pdes ◽  
Monotonicity Condition ◽  
Stochastic Monotonicity ◽  
Monotone Coefficients ◽  
Terminal Time

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.

Reflected backward stochastic differential equations with time-delayed generators

2018 ◽  
Vol 26 (1) ◽  
pp. 11-22
Author(s):  
Navegué Tuo ◽  
Harouna Coulibaly ◽  
Auguste Aman
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Penalization Method ◽  
One Dimensional

AbstractThis paper is devoted to establish an existence and uniqueness result of one-dimensional reflected backward stochastic differential equations with time-delayed generators (RBSDEs with time-delayed generators, in short). Our proof is based on approximation via a penalization method.

scholarly journals Existence and Uniqueness of Solutions for a Class of Nonlinear Stochastic Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Iryna Volodymyrivna Komashynska
Keyword(s):  
Differential Equations ◽  
Diffusion Process ◽  
Stochastic Differential Equations ◽  
Successive Approximation ◽  
Diffusion Coefficients ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Uniqueness Of Solutions ◽  
Nonlinear Stochastic Differential Equations

By using successive approximation, we prove existence and uniqueness result for a class of nonlinear stochastic differential equations. Moreover, it is shown that the solution of such equations is a diffusion process and its diffusion coefficients are found.

scholarly journals Fuzzy stochastic differential equations driven by fractional Brownian motion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Marek T. Malinowski ◽  
M. J. Ebadi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Stochastic Integral ◽  
Long Range Dependence ◽  
World Systems

AbstractIn this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

scholarly journals On invariant measures of nonlinear Markov processes

1993 ◽  
Vol 6 (4) ◽  
pp. 385-406 ◽  
Author(s):  
N. U. Ahmed ◽  
Xinhong Ding
Keyword(s):  
Markov Process ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Nonlinear Markov Processes

We consider a nonlinear (in the sense of McKean) Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.

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