scholarly journals INFINITELY MANY BROWNIAN GLOBULES WITH BROWNIAN RADII

2010 ◽  
Vol 10 (04) ◽  
pp. 591-612
Author(s):  
MYRIAM FRADON ◽  
SYLVIE RŒLLY
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Strong Solution ◽  
Local Time ◽  
Existence And Uniqueness ◽  
Infinite System ◽  
Time Dependent ◽  
Initial Condition ◽  
Infinite Dimensional ◽  
Time Existence

We consider an infinite system of non-overlapping globules undergoing Brownian motions in ℝ3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.

STOCHASTIC EQUATIONS AND QUASI-INVARIANCE ON INFINITE PRODUCT GROUPS

1999 ◽  
Vol 02 (02) ◽  
pp. 283-288 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
ALEXEI DALETSKII
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Lie Group ◽  
Existence And Uniqueness ◽  
Infinite Product ◽  
Stochastic Equations ◽  
Compact Lie Group ◽  
Infinite Dimensional ◽  
Countable Power ◽  
Infinite Dimensional Lie Group

A stochastic differential equation on an infinite-dimensional Lie group G constructed as the countable power of a compact Lie group G is considered. The existence and uniqueness of the solutions and quasi-invariance of their distribution are proved.

scholarly journals Lp (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals

2014 ◽  
Vol 15 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Li-Shun Xiao ◽  
Sheng-Jun Fan ◽  
Na Xu
Keyword(s):  
Differential Equation ◽  
Weak Convergence ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Additional Assumption ◽  
Backward Stochastic Differential Equation ◽  
Time Interval ◽  
Time Intervals ◽  
Lipschitz Continuous ◽  
General Time

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equation in Lp (p ≥ 1). We first study the existence and uniqueness for Lp (p > 1) solutions by the method of convolution and weak convergence when the generator is monotonic in y and Lipschitz continuous in z both non-uniformly with respect to t. Then we obtain the existence and uniqueness for L1 solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.

BSDE with rcll reflecting barrier driven by a Lévy process

2020 ◽  
Vol 28 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Mohamed El Jamali ◽  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
American Option ◽  
Levy Process ◽  
Fair Price ◽  
Penalization Method ◽  
Uniqueness Of A Solution

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

scholarly journals Centre-of-mass like superposition of Ornstein–Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

2018 ◽  
Vol 21 (5) ◽  
pp. 1420-1435 ◽  
Author(s):  
Mirko D’Ovidio ◽  
Silvia Vitali ◽  
Vittoria Sposini ◽  
Oleksii Sliusarenko ◽  
Paolo Paradisi ◽  
...  
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Gaussian Process ◽  
Relaxation Times ◽  
Random Variable ◽  
Fractional Diffusion ◽  
Time Dependent ◽  
Centre Of Mass ◽  
Time Scaling

Abstract We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.

Fractional anticipated BSDEs with stochastic Lipschitz coefficients

2018 ◽  
Vol 26 (3) ◽  
pp. 143-161
Author(s):  
Ahmadou Bamba Sow ◽  
Bassirou Kor Diouf
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Hurst Parameter ◽  
Uniqueness Of A Solution

Abstract In this paper, we deal with an anticipated backward stochastic differential equation driven by a fractional Brownian motion with Hurst parameter {H\in(1/2,1)} . We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and prove a comparison theorem in a specific case.

scholarly journals Monte-Carlo Galerkin Approximation of Fractional Stochastic Integro-Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abdallah Ali Badr ◽  
Hanan Salem El-Hoety
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Galerkin Approximation ◽  
Integro Differential Equation ◽  
Uniqueness Of The Solution ◽  
Time Continuum

A stochastic differential equation, SDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper reformulates the fractional stochastic integro-differential equation as a SDE. Existence and uniqueness of the solution to this equation is discussed. A numerical method for solving SDEs based on the Monte-Carlo Galerkin method is presented.

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