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ANOVA FOR DIFFUSIONS AND ITO PROCESSES
 SUBMITTED TO THE ANNALS OF STATISTICS
"... Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual in this re ..."
Abstract

Cited by 34 (12 self)
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Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual
continuous Itô process
, 2008
"... In this paper, we consider a ddimensional continuous Itô process which is observed at n regularly spaced times on a given time interval [0,T]. This process is driven by a multidimensional Wiener process and our aim is to provide asymptotic statistical procedures which give the minimal dimension of ..."
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In this paper, we consider a ddimensional continuous Itô process which is observed at n regularly spaced times on a given time interval [0,T]. This process is driven by a multidimensional Wiener process and our aim is to provide asymptotic statistical procedures which give the minimal dimension
ANOVA FOR DIFFUSIONS AND ITÔ PROCESSES 1
"... Itô processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such Itô processes. We are interested in the quadratic variation (integrated volatility) of the residual in this r ..."
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Itô processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such Itô processes. We are interested in the quadratic variation (integrated volatility) of the residual
Discrete sampling of functionals of Itô processes.
, 2004
"... For a multidimensional Itô process (Xt)t≥0 driven by a Brownian motion, we are interested in approximating the law of ψ () (Xs)s∈[0,T] , T> 0 deterministic, for a given functional ψ using a discrete sample of the process X. For various functionals (related to the maximum, to the integral of the p ..."
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For a multidimensional Itô process (Xt)t≥0 driven by a Brownian motion, we are interested in approximating the law of ψ () (Xs)s∈[0,T] , T> 0 deterministic, for a given functional ψ using a discrete sample of the process X. For various functionals (related to the maximum, to the integral
ON THE FIRST TIME THAT AN ITO PROCESS HITS
"... Abstract. This work deals with first hitting time densities of Ito processes whose local drift can be modeled in terms of a solution to Burgers equation. In particular, we derive the densities of the first time that these processes reach a moving boundary. We distinguish two cases: (a) the case in w ..."
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Abstract. This work deals with first hitting time densities of Ito processes whose local drift can be modeled in terms of a solution to Burgers equation. In particular, we derive the densities of the first time that these processes reach a moving boundary. We distinguish two cases: (a) the case
1 Ito Processes with Finitely Many States of Memory
, 2007
"... We show that Ito processes imply the FokkerPlanck (K2) and Kolmogorov backward time (K1) partial differential eqns. (pde) for transition densities, which in turn imply the ChapmanKolmogorov equation without approximations. This result is not restricted to Markov processes. We define ‘finite memory ..."
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Cited by 1 (0 self)
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We show that Ito processes imply the FokkerPlanck (K2) and Kolmogorov backward time (K1) partial differential eqns. (pde) for transition densities, which in turn imply the ChapmanKolmogorov equation without approximations. This result is not restricted to Markov processes. We define ‘finite
Matching Statistics of an Itô Process by a Process of Diffusion Type
, 2010
"... Suppose we are given a multidimensional Itô process, which can be regarded as a model for an underlying asset price together with related stochastic processes, e.g., volatility. The drift and diffusion terms for this Itô process are permitted to be arbitrary adapted processes. We construct a weak s ..."
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Cited by 4 (0 self)
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Suppose we are given a multidimensional Itô process, which can be regarded as a model for an underlying asset price together with related stochastic processes, e.g., volatility. The drift and diffusion terms for this Itô process are permitted to be arbitrary adapted processes. We construct a weak
Mimicking an Itô process by a SOLUTION OF A STOCHASTIC DIFFERENTIAL EQUATION
, 2012
"... Given a multidimensional Itô process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the Itô process at each fixed time. Moreover, we show how to match the distributions at each fixed time of ..."
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Cited by 4 (0 self)
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Given a multidimensional Itô process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the Itô process at each fixed time. Moreover, we show how to match the distributions at each fixed time
Boundary value problems for functionals of Ito processes
 Theory of Probability and its Applications 36
, 1992
"... ar ..."
The Valuation of Options for Alternative Stochastic Processes
 Journal of Financial Economics
, 1976
"... This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have nol been used in previous models. The technique is applied lo these processes to find explicit option valuation formulas, ..."
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Cited by 661 (4 self)
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This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have nol been used in previous models. The technique is applied lo these processes to find explicit option valuation formulas
Results 1  10
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