Ambit Processes and Stochastic Partial Differential Equations

Asymptotic Problems for Stochastic Processes and Corresponding Partial Differential Equations

Title of dissertation: ASYMPTOTIC PROBLEMS FOR STOCHASTIC PROCESSES AND CORRESPONDING PARTIAL DIFFERENTIAL EQUATIONS Lucas Tcheuko, Doctor of Philosophy, 2014 Dissertation directed by: Professor Mark Freidlin & Professor Leonid Koralov Department of Mathematics We consider asymptotic problems for diffusion processes that rely on large deviations. In Chapter 2, we study the long time behavior (a...

Stochastic Partial Differential Equations

Time-homogeneous Affine State Processes for Stochastic Partial Differential Equations

The goal of this paper is to clarify for which starting points the state processes of a stochastic partial differential equation with an affine realization are time-homogeneous. We will illustrate our results by means of the HJMM equation from mathematical finance.

Backward Stochastic Differential Equations Associated with Lévy Processes and Partial Integro-differential Equations

In this paper, we deal with a class of backward stochastic differential equations driven by Teugels martingales associated with a Lévy process (BSDELs). The comparison theorem is obtained. It is also shown that the solution of BSDE provides a viscosity solution of the associated system with partial integro-differential equations.

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...