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Generalized Stochastic Processes
Compact Textbooks in Mathematics, 2018Stefan Schaffler
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A GENERAL SUBORDINATED STOCHASTIC PROCESS FOR DERIVATIVES PRICING
International Journal of Theoretical and Applied Finance, 2001A general subordinated stochastic process is proposed to model the dynamics of the underlying asset of an option. We prove that this class of models can be considered generically as the limit of discrete time models in which the number of transactions is random. We also derive several results for the valuation of contingent claims in this framework. In
Lesne, J., Prigent, Jean-Luc
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Stochastic Processes in General
1996Let (Ω, F, P) be a probability space, (E, e) a measurable space, and Σ an arbitrary set. A stochastic process is a family X = { X t : t ∈ Σ} of random variables X t : Ω ↦ E. The space (E, e) is refered to as the state space of X. Given a point w in the sample space Ω the mapping t ↦ X t (ω) is called a trajectory or realization or sample path of the ...
Andrei N. Borodin, Paavo Salminen
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Generalized Stochastic Processes
SSRN Electronic Journal, 2009We introduce a general stochastic process that is not necessarily a diffusion/jump process and the random variable is not necessarily normally distributed.
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A Stochastic Process Generated by the Lévy Laplacian
Acta Applicandae Mathematica, 2000Let \(\Phi\) be a generalized white noise functional. The \(S\)-transform is defined as \(S[\Phi](\xi)=\exp(-{{1}\over{2}}\langle \xi,\xi\rangle)\) \(\langle \Phi(\cdot),\exp\langle \cdot,\xi\rangle\rangle\), where \(\exp\langle \cdot,\xi\rangle\) is a testing functional generated by a function \(\xi\) on the finite interval \(T\). The Lévy Laplacian \(
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Modelling Data with Stochastic Generative Processes
2020Learning and modelling complex data with generative models is a prominent research topic in modern artificial intelligence since generative models empower us to answer fundamental and important research questions into the generative processes of algorithmic intelligence.
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NONLINEAR STOCHASTIC WAVE EQUATION WITH COLOMBEAU GENERALIZED STOCHASTIC PROCESSES
Mathematical Models and Methods in Applied Sciences, 2002Colombeau generalized stochastic processes are introduced in order to solve nonlinear wave and Klein–Gordon equations with stochastic processes. Particular cases include one- and three-dimensional wave and Klein–Gordon equations with Lipschitz and cubic nonlinearities.
Nedeljkov, Marko +1 more
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On stochastic processes generated by a stochastic intensity function
Scandinavian Actuarial Journal, 1971Abstract In this paper we are going to study some properties of a point process, which has been proposed by Cramer [4] as a model of the claims arising in an insurance company. This process has been studied by Cox in a different context. A few elementary results, concerning moments, are given in Cox and Lewis [2].
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