摘要:

Following a detailed discussion of the linear Kalman–Bucy filter for the l–dimensional case a description of Zakai nonlinear filtering of then-dimensional logistic is presented. Explicit formulas for thec∞-densities for least squares estimation of growth variables conditioned on continually updated community production or consumption records, are obtained. Application is made to a model of the myxomatosis disease in European wild rabbits and to a coral growth model with predation. Extensive use is made of the techniques of linear stochastic partial differential equations developed by H. Kunita, especially backward stochastic calculus and decomposition techniques

ISSN:0736-2994    

DOI:10.1080/07362999008809209

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We approximate a k:–dimensional Brownian motion w by a process wnwith piecewise linear trajectories. The solutions of the partial differential equationconverge to the solutions of the corresponding Stratonovich one:. This is proved by emlploying the Feynman–Kac formula for stochastic partial differential equations. In this way the problem of convergence is reduced to the demonstration of a suitabie convergence of solutions of the related ordinary stochastic differential equations which itself is a generalization of known convergence results

ISSN:0736-2994    

DOI:10.1080/07362999008809210

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Two sets of expert decision makers are presented with the same query. Their responses to this query are represented by fuzzy sets which induce a generalized basic probability assignment (b.p.a.) over the class of fuzzy sets of the frame of discernment (⋀). The opinions of the two sets of experts are then polled in a conservative manner. The main result establishes a homomorphism from the class of experts with the operation defined by conservative polling into the class of generalized b.p.a.'s over the fuzzy subsets of ⋀ in which the combination operation is defined by Oblow's generalization of the Denlpster–Shafer rule. This result extends to other types of polling

ISSN:0736-2994    

DOI:10.1080/07362999008809211

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

While stochastic product integration w.r.t finite rank Hilbert Schmidt operator (K2-) valued semimartingales has received reasonable attention, there is no work, to date, dealing with infinite dimensional semimartingales. We initiate here a theory of stochastic product integration of K2-predictable processes w.r.t the exponential of a K2-Brownian motion. To understand the estimations involved, we start with a finite rank Brownian motion β while keeping the integrand in K2and then we continue with infinite dimellsioilal Brownian motion. In order to apply our stochastic product integral to solve Doleans–Dade – Protter type linear stochastic equations, we also need to, and therefore, define the Ito integral in the space HS. We finally give the stochastic product integral construction of the solution of a linear stochastic equation. All this is done in the uniform operator topology case. The more difficult unbounded operator case is the subject matter of the final part of this series

ISSN:0736-2994    

DOI:10.1080/07362999008809212

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

For a class of stochastic differential equations with anticipating evolution systems onRd, the “evolution solution” is defined similarly as in the usual case, replacing the Itô stochastic integral term by a Skorohod integral plus an additional term which involves the Malliavin derivation operator. It is proved that strong solutions and evolutions solutions of these equations are equivalent

ISSN:0736-2994    

DOI:10.1080/07362999008809213

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0736-2994    

DOI:10.1080/07362999008809208

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor