Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions

Pathwise stationary solutions of stochastic Burgers equations with L[0, 1]-noise and stochastic Burgers integral equations on infinite horizon

In this paper, we show the existence and uniqueness of the stationary solution u(t, ω) and stationary point Y (ω) of the differentiable random dynamical system U : R×L[0, 1]×Ω → L[0, 1] generated by the stochastic Burgers equation with L[0, 1]-noise and large viscosity, especially, u(t, ω) = U(t, Y (ω), ω) = Y (θ(t, ω)), and Y (ω) ∈ H[0, 1] is the unique solution of the following equation in L[...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component∗

We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded Hölder term; in spite of this, due to the space-time white noise it is possible to prove pathwise uniqueness. The proof is based on a detailed analysis of the associated Kolmogorov equation. The model includes examples not covered by the previous works based on Hilb...

The Study of Triple Integral Equations with Generalized Legendre Functions

Pathwise Stochastic Control Problems and Stochastic HJB Equations

In this paper we study a class of pathwise stochastic control problems in which the optimality is allowed to depend on the paths of exogenous noise (or information). Such a phenomenon can be illustrated by considering a particular investor who wants to take advantage of certain extra information but in a completely legal manner. We show that such a control problem may not even have a “minimizin...