Stochastic Differential Equations for the limiting processes
On solutions to backward stochastic partial differential equations for Lévy processes
... resulting processes H ( i ) = { H t ( i ) , t ≥ 0 } are called the orthonormalized ith-power-jump ...a stochastic differential equation (SDE, for short) driven by a general Lévy process (taking into ...
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Stability of the Stochastic Differential Equations
... of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its ...concrete stochastic dynamical systems, conditions of existence the ...
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Optimal control of semi-Markov processes with a backward stochastic differential equations approach
... is, stochastic ker- nels or measurable functions that depend only on the last jump time and post jump ...jump processes is for instance [20], [19], [23], [24], ...semi-Markov processes, we are able ...
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Stochastic Taylor Methods for Stochastic Delay Differential Equations
... via stochastic delay differential equations ...from stochastic Taylor expansions with time delay showed a strong order of convergence of ...double stochastic integral involving time ...
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Quasilinear Stochastic Partial Differential Equations
... Quasilinear stochastic PDE’s occur in applications such as the stochastic Navier-Stokes equation for which there is a complete answer to existence and uniqueness of ...The stochastic term in each of ...
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Stochastic differential equations and integrating factor
... The aim of this paper is the analytical solutions the family of first-order nonlinear stochastic differ- ential equations. We define an integrating factor for the large class of special nonlinear ...
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Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes
... 1.25 Exchange rate EUR / CHF Figure 1.1: Behavior of the exchange rate of EUR/CHF from December 1st, 2014 to June 1st, 2015 (data source: yahoo finance). We look now at an example from finance. In Figure 1.1 the behavior ...
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Generalized backward doubly stochastic differential equations driven by Lévy processes with non-lipschitz
... for stochastic vis- cosity solutions of semi-linear SPDEs with a Neumann boundary ...of stochastic partial differential integral equations (SPDIEs in short) with a nonlinear Neumann boundary ...
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Stochastic control representations for penalized backward stochastic differential equations
... Penalized BSDE is nothing but a random time discretization of the optimal stopping representation for the corresponding reflected BSDE, where the time is discretized by Poisson arrival times. Acknowledgments. The author ...
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Stochastic Runge-Kutta method for stochastic delay differential equations
... specifically stochastic Runge–Kutta with time delay, we propose to derive SRK for SDDE in this research as well as to approximate the strong solution of SDDE via this ...of differential equations, ...
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Discontinuous Quantum Stochastic Differential Equations and The Associated Kurzweil Equations
... evolution processes in which states are changed abruptly at certain moments of time, involving such fields as biology, medicine, economics, mechanics, electronics, ...impulsive differential systems are very ...
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Malliavin calculus for backward stochastic differential equations and stochastic differential equations driven by fractional Brownian motion and numerical schemes
... of stochastic differential equations (SDEs, for short) driven by Brownian motion is essentially based on the method of time discretization and has a long ...
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The Osgood condition for stochastic partial differential equations
... Theorem 1.3. Suppose that Assumption 1.1 holds. If almost surely the solution to (1.2) blows up in finite time then b satisfies the Osgood condition (1.3). Together with the result of Bonder and Groisman, this can be ...
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Stability of stochastic differential equations in infinite dimensions
... functional differential equations such as differential equations with memory, even with constant delays, since the history of the process must be taken into ...the stochastic energy ...
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Stochastic differential equations in a scale of Hilbert spaces
... The aim of the present work is to extend Ovsyannikov’s method to the case of stochastic differential equations. We require the drift f to be a map from X α to X β for any α < β and satisfy a ...
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Multidimensional stochastic differential equations with distributional drift
... of stochastic differential equations with generalized coefficients, it is difficult to quote them all: in particular, we refer to the case when b is a measure, [4, 7, 18, ...solving stochastic ...
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Asymptotic behaviours of stochastic differential delay equations
... on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this ...tic differential delay ...on stochastic asymptotic stability, which enable us ...
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Optimization governed by stochastic partial differential equations
... SPDEs are partial differential equations for which the input data (i.e. forcing terms, diffu- sion/advection/reaction coefficients, domain) are uncertain. This uncertainty could arise [r] ...
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Recursive Bayesian inference on stochastic differential equations
... the processes are modeled as Itô stochastic differential equations (SDE) driven by Brownian motions and the measurements are modeled as non-linear functions of the state, which are corrupted ...
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Introduction to Stochastic Differential Equations (SDEs) for Finance
... 3 The Black-Scholes Theory This section builds a pricing theory around the assumptions of no-arbitrage with perfect liquidity and trades occurring in continuous time. The Black-Scholes model is a complete market, and ...
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