scholarly journals STOCHASTIC INTEGRATION WITH RESPECT TO THE CYLINDRICAL WIENER PROCESS VIA REGULARIZATION

2013 ◽  
Vol 16 (03) ◽  
pp. 1350024 ◽  
Author(s):  
CHRISTIAN OLIVERA
Keyword(s):  
Wiener Process ◽  
Stochastic Integral ◽  
Existence Of Solution ◽  
Stochastic Integration ◽  
Cylindrical Wiener Process ◽  
Classical Integral

Following the ideas of F. Russo and P. Vallois, we use the notion of forward integral to introduce a new stochastic integral respect to the cylindrical Wiener process. This integral is an extension of the classical integral. As an application, we prove existence of solution of a parabolic stochastic differential partial equation with anticipating stochastic initial date.

scholarly journals Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Gregorio Díaz ◽  
Jesús Ildefonso Díaz
Keyword(s):  
Energy Balance ◽  
Wiener Process ◽  
Climate Models ◽  
Random Parameter ◽  
Parabolic Problems ◽  
Change Of Variables ◽  
Wiener Processes ◽  
Cylindrical Wiener Process ◽  
The Stability ◽  
Suitable Change

<p style='text-indent:20px;'>We consider a class of one-dimensional nonlinear stochastic parabolic problems associated to Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing. Our results use in an important way that, under suitable assumptions on the Wiener processes, a suitable change of variables leads the problem to a pathwise random PDE, hence an essentially "deterministic" formulation depending on a random parameter. Two applications are also given: the stability of solutions when the Wiener process converges to zero and the asymptotic behaviour of solutions for large time.</p>

AN EXTENDED STOCHASTIC INTEGRAL AND A WICK CALCULUS ON PARAMETRIZED KONDRATIEV-TYPE SPACES OF MEIXNER WHITE NOISE

2008 ◽  
Vol 11 (04) ◽  
pp. 541-564 ◽  
Author(s):  
N. A. KACHANOVSKY
Keyword(s):  
White Noise ◽  
Stochastic Equation ◽  
Stochastic Integral ◽  
Holomorphic Functions ◽  
Generalized Functions ◽  
Wick Product ◽  
Stochastic Integration ◽  
Type Spaces ◽  
Wick Calculus

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".

scholarly journals Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators

2020 ◽  
Author(s):  
Tomasz Kosmala ◽  
Markus Riedle
Keyword(s):  
Evolution Equation ◽  
Banach Spaces ◽  
Lévy Processes ◽  
Stochastic Integral ◽  
Levy Processes ◽  
Integration Theory ◽  
Stochastic Evolution Equation ◽  
Stochastic Integration ◽  
Stochastic Evolution ◽  
Existence Of A Solution

AbstractWe introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for $$p\in [1,2]$$p∈[1,2]. The space of integrands consists of p-summing operators between Banach spaces of martingale type p. We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical Lévy process.

Stochastic Integrals

2019 ◽  
pp. 43-66
Author(s):  
Tomas Björk
Keyword(s):  
Wiener Process ◽  
Stochastic Integral ◽  
Stochastic Integrals ◽  
Itô Formula ◽  
Martingale Theory ◽  
Ito Formula

We introduce the Wiener process, the Itô stochastic integral, and derive the Itô formula. The connection with martingale theory is discussed, and there are several worked-out examples

On Delayed Logistic Equation Driven by Fractional Brownian Motion

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Nguyen Tien Dung
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Approximate Method ◽  
Explicit Expression ◽  
Stochastic Integral ◽  
Logistic Equation ◽  
The Other ◽  
Stochastic Integration

In this paper we use the fractional stochastic integral given by Carmona et al. (2003, “Stochastic Integration With Respect to Fractional Brownian Motion,” Ann. I.H.P. Probab. Stat., 39(1), pp. 27–68) to study a delayed logistic equation driven by fractional Brownian motion which is a generalization of the classical delayed logistic equation. We introduce an approximate method to find the explicit expression for the solution. Our proposed method can also be applied to the other models and to illustrate this, two models in physiology are discussed.

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