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This paper discusses an invariance principle for a Brownian motion with drift coefficient /c/4 in a white noise environment under the assumption that K is large. Our method clarifies the relation between the environment-wise invariance principle discussed in [7] and the present result (the invariance principle in random environment). Introduction Let W be the space of continuous functions on R vanishing at 0 that is equipped with the Wiener measure P. For an element w e W let us denote by wκ the element of W defined by wκ(x) = w(x) — (κx/2) where K: is a given positive constant. For w e W, Pw denotes the probability measure on Ω = C[0, oo ) such that Xx = {ω(i),t > 0,PW} is a diffusion process with generator starting at 0, where ω(t) is the value of a function ω(e fl) at time t. We regard ω(t) as a process defined on the probability space { W x Ω, £?} where 9(dwdω) — P(dw)Pw(dω). Then symbolically dω(t) = dB(t}+^dt-^w'((o(i)}dt, where B(t) is a standard Brownian motion independent of the white noise {H/(X)}. We call the process X = {ω(i),t > 0,0*} a Brownian motion with drift in a white noise environment; in [2] [6] [7] it is called a diffusion process in a Brownian environment with drift. The present authors obtained some limit theorems for X in [2] (see [8] for further results; see also [6] for a brief survey on related problems), which are analogous to those of [3] and [5]; however, some problems remain open. The present paper is a continuation of [7] and 1991 Mathematics Subject Classification. 60J60

Invariance principle for a Brownian motion with large drift in a white noise environment